All positive Beta exponents in a binomial logistic regression

I'm running a regression in which the predictor is a categorical measure of living arrangement (1=two parent household, 2 = single parent, etc). There are 8 total categories in this variable. I'm using them to predict a binary categorical outcome (1=yes and 2=no).

The results I'm getting all have positive B coefficients and Exp(B) values greater than one. I'm interpreting this to mean that, for example, two parent households are more likely to score a 2 than all other living arrangements. However, if this is the case for ALL categories, wouldn't this be impossible? Not sure how every category can be more likely to have the same outcome than every other category.

I'm new to this type of analysis so it's very possible that I'm interpreting the outcome incorrectly. Any help would be greatly appreciated.

• What program are you using? Some programs treat the coding of your response variable differently. In general, it's typical to manually set yes $=1$ and no $=0$. By the way, there is nothing concerning with having $exp(\hat{\beta}) \gt 1$. – StatsStudent Feb 5 at 4:44
• If you can add the actual output that would be helpful. – Yuval Spiegler Feb 5 at 4:49

Categorical independent variables need to be parameterized - there are various methods, the most common are dummy coding and effect coding and searching on those terms will give a lot of information, both here and elsewhere. Any decent statistics program (R, SAS, SPSS etc) will do this for you, provided that you write the code correctly (e.g. in SAS, you need a class statement, in R you need to use factor) but, unfortunately, the defaults aren't entirely uniform across programs.